holds for non-negative \(u_i \in L^\varphi (\Omega )\) .
This is an easy consequence of [1]}, which states that there exists \(c \geqslant 1\)  such that
\(\Big {\Vert } \sum _{i=1}^\infty u_i \Big {\Vert }_\varphi \leqslant c\sum _{i=1}^\infty \Vert u_i\Vert _\varphi .\) 
